Function Festival
Fall 2000
Opening Scene with Grav
Ocity: Ladies and gentleman, students and teachers, Investigators of all kinds - we have found the first gravitom in captivity, "Grav".Scientists thought one or more existed but did not know how many legs it had nor its surface area. I, "Ocity", wish to introduce you to the wonderment of my "Function Festival" where you may "guess" each step of our path - or - you may not!
Ocity: At my command the great "Grav" will invert ~ an action never seen by a human before (except for those of us in dress rehearsal).
Grav: I can't escape the curves of space. Straight lines I walk and circles I trace.
Ocity: OK "GRAV" INVERT!!!! You may think you are hearing a sound or even a song coming from "Grav" - well - yes - you - are.
Grav: I can't escape the curves of space. Straight lines I walk and circles I trace.
Ocity: BACK "GRAV" - Back "O Great One" - - Good (Ocity turns to the Investigators as "Grav" inverts and postulates) We do not know which is the NATURAL STATE for "Grav". Inside Out - Outside In - Are those OPPOSITES or the same(?) - maybe we should consider INSIDE IN or OUTSIDE OUT instead?? What do you Investigators think? Oh well - never mind - you are just beginning to muse about that OPPOSITE stuff for yourself - right!
Ocity: Tim - Do we have time for this?
Tim: We do we have time for a few function presentations if "Grav" cooperates
Materials:
1. Chart A to hang over
moving sidewalk handrail showing d = r x t (have examples of a constant
distance with the affect that rate changes
have
on the time distance= rate x time 12 ft = 12 ft/min x ? 1 min.)).
2. Chart B showing the
summation of rates (the sidewalk rate plus the running rate)
Actors:
1. Two to make the moving sidewalk (machine person #1 and #2).
2. Two to walk on the sidewalk and talk about it (walker #1 and #2).
3. One to run on the sidewalk (runner).
Script:
Walker #1: You are really going to enjoy your trip to Spain.
Walker #2: But, I’m not going to enjoy that long plane ride over.
Walker #1: To bad you’re not taking the Concord. That plane has such a fast rate that the time is much less.
Walker #2: When I’m a millionaire, that’s the way I’m going.
Walker #1: Is that what I think it is? I’ve never seen one in person before.
Walker #2: You mean a moving sidewalk?
Moving sidewalk #1 (ms #1): Look out here come some more tourist
Moving sidewalk #2 (ms #2): I hope they just stand on us and don’t and don’t go running on us.
Ms #1:They don’t
seem to understand that we always move at the same rate or speed
(12feet/minute) and since we are 12 feet long
we
always give a one minute ride.
(Put chart A over handrail)
Ms #2: Yes, but if they are late they want a faster ride and to decrease the time they must increase the rate.
Ms. #1: But how can that happen, we always travel at the same rate?
Ms. #2: Yes, but if they walk or run then their rate is added to our rate for a total rate that is faster.
Ms #1: So, then their ride will be less than one minute.
Ms #2: Exactly, if they walk on us at
a rate of 12 feet/minute and we move 12 feet/minute then their total rate
is 24 feet/minute and the
@@@@@@ 12
foot distance is covered in ½ minute instead of one minute.
(Put chart B over handrail)
Ms #1: I understand better now why people walk or run on us but it still hurts my back.
(Walkers step on and the sidewalk grimaces and grumbles.)
Walker #1: I’m glad we got to the airport early so we don’t have to rush.
Walker #2: Here comes someone who didn’t get here early.
(Sidewalk exaggerates pain of being run on.)
Runner: Excuse me; I’m late for my plane.
Ms. #1: I sure hope the ½ minute she saves gets her to her plane on time.
Walker #1: Be careful getting off the sidewalk. You need to start walking right away or you might fall. Remember you are still moving at 20 feet/minute as you leave the moving sidewalk and if you don’t start walking at that speed your body will be moving faster than your feet and you could fall.
Walker #2: Like when my bike hit the curb and stopped but I kept going over the handlebars?
Walker #1: Precisely.
Thad:
Ladies and gentlemen, if you could now feast your eyes on this table
where a new event is about to take place! Note how the sphere is
being covered by one of these three cones. Dawn is going to graph
where the sphere is as Ashley tries to trick him by moving it.
Look! Ashley has moved the cone covering the sphere to square
two. Dawn is graphing it! Now Ashley has moved the sphere to
square one. Ashley needs to move faster if she wants to trick
Dawn! Wow! Ashley keeps moving the sphere and Dawn has no
trouble graphing it!
Cliff: So, what you're saying is
that this line tells me everywhere the sphere has been, and where it is
now? How do I know the sphere is where the graph says it
is?
Thad: Well, it appears that our moment of truth
has arrived! Ashley, according to the graph Dawn made, the sphere is
now under the cone in square three. Can you show us?
(Ashley lifts the cone) Amazing! Dawn was right!
Lets try this again. Only this time, there are four cones.
Ashley sure is moving faster this time! Oh no! Dawn isn't fast
enough! (Dawn starts to go crazy on the graph.) Do you
guys know where the sphere is now?
Ashley: Is it
under cone one? (point and pose) Or cone two? (point
and pose) Or did I stop the sphere under cone three?
(point and pose)
Thad: Wait! I think
they're saying it's under cone two, Ashley! Let's try that.
Wonderful! Maybe you guys could help us keep track again ...
Actors:
3
people are juggling
2 people
playing catch
2 are holding
the sign
4 to jump up with
equation.
Script:
Student #1: Hey haw are
you?
#2: Fine, what's
up?
#1: I need to ask you
something.
#2:
Shoot.
#1: Today in math class we talked about (with much
hesitation)
par-para-parabolas?
#2:
Oh-parabolas.
#1:
Ya.
#2: Do you remember what you teacher told you about
them?
#1: The equation is Y equals, uh, I don't remember (4
holding a sign). It's
y=x^2
#1: Oh yea -
Y=x^2
#2: O.K. Good! Parabolas are basically a shape that
looks like this (makes one with hands), see over here
(points to sheet). This line is @@@@@ the graph of the equation- Y=x^2, and you can
find parabolas
everywhere.
#1: What do you mean you can find parabolas everywhere. You can
never use math outside of class,
right?
#2: Of course not, math is fun, and it has many
applications in life. It is all around in our
world.
#1: Oh-so if that is true-where is parabola
here.
#2: Well, look right here at these people that are juggling, the
balls that they are throwing are making parabolas. Do you see
them?
#1: I think
so.
#2: Why are you so unsure of yourself? Here make a shape
of a parabola with your hand. (They do it
together.)
#2: Now-try to put that in sync' with the
jugglers.
#1. Oh-Oh I see it now- (Goes to each
juggler and points to
parabolas)
#2: Good - now you got
it!
#1: Yea - and here is a parabola over here - where these
two are playing catch. See
it.
#2: Yes -
good!
#1: TO AUDIENCE Can you guys think of what other
things may make a parabola?
Dawn:
Hello everyone, welcome to our magic show! We are going to show you
some wonderful magic tricks. (And we show them a cylinder.)
This cylinder has two kinds of figures (We open the cylinder and
the cylinder becomes both a circle and a rectangle). This cylinder
was made by a circle and a rectangle and also the helix is just a straight line. It is almost like magic, isn't it?
But now I am going to show you real magic. (And Paul goes to the
back of the parachute, and they put the small parachute over him.
So that Paul can escape from the parachute to behind the curtains.
They are spinning the cylinder after two seconds. Some music is coming from behind. When the parachute is lifted Paul is gone.Some of the calculus students
sit with the elementary school students and say, "where is he, where
is he?" Then, Ash gives signal to Wayne and Wayne appears from the
crowd).
Dawn: How was your journey?
Wayne: It was a good trip, too short though.
Dawn: Sometimes
math looks like magic, but it is not magic at all. If you know how to do
it then it is more like a trick. Now we shall show you how we did Paul: We are twins.
Dawn: Mm . . . I got it.
Paul and Wayne (together): Now our class members will show you .....
the trick.
(and Paul comes out from behind the curtains).
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